# Longest paths in 2-edge-connected cubic graphs

## TL;DR

This paper establishes bounds on the longest paths in 2-edge-connected cubic graphs, showing that such graphs have paths of at least logarithmic squared length, but some graphs limit paths to similar upper bounds.

## Contribution

It provides almost tight bounds on the maximum path length in 2-edge-connected cubic graphs, advancing understanding of their structural properties.

## Key findings

- Lower bound: paths of length Omega(log^2 n / log log n)
- Upper bound: paths of length O(log^2 n) in some graphs
- Almost tight bounds on path lengths in these graphs

## Abstract

We prove almost tight bounds on the length of paths in $2$-edge-connected cubic graphs. Concretely, we show that (i) every $2$-edge-connected cubic graph of size $n$ has a path of length $\Omega\left(\frac{\log^2{n}}{\log{\log{n}}}\right)$, and (ii) there exists a $2$-edge-connected cubic graph, such that every path in the graph has length $O(\log^2{n})$.